29 



Equator. This conception appears, however, to compUcate rather 

 than to simpUfy a consideration of the tidal components and is not 

 herein pursued. 



51. Comhination oj components. — A consideration of the manner in 

 which two or more components combine with each other will afford 

 a basis for the selection of the speeds of the particular components 

 which reproduce the tide at any station as it varies with the changing 

 positions and distances of the moon and sun. 



Taking the two components: 



yi=Ai cos (rti^+ai) y2 = A2 cos {a-it-^ao^ (30) 



let CPi and CP^ (fig. 17) be the positions of their generating radii at 



FionRE 17.— Resultant of components of unequal speeds. 



any instant of time. Completing the parallelogram CP1P3P2 it is 

 at once apparent that the projection on the Y axis of the resultant 

 vector CP3 is the algebraic sum of the ordinates of the two compo- 

 nents yi and ?/2 at that instant. This resultant vector CP3 will there- 

 fore generate the tide curve of the resultant of the 

 two components, as shown on the right of the 

 figure. 



If CPi, CP2, and CP3 (fig. 18), are the generat- 

 ing radii of three components at any instant, 

 the length and position of the resultant vector 

 is given by the line CP, found by drawing P1P2 

 parallel and equal to CP2, and Po P parallel 

 and equal to CP3. The resultant vector of any 

 number of components may be drawn in a similar manner. 



52. Two components of the same speed. — If two components have 

 the same speed, the angle between the generating yadii CPi and CP2 

 (fig. 17), remains constant, the parallelogram CP1P3P2 does not change 

 its shape as the radii rotate around O, and the resultant vector CP3 

 therefore remains of constant length and rotates at the constant 

 speed of the two components. It will therefore generate a sinusoidal 

 curve as shown in figure 19. 



Figure IS. -liesultant vector 

 of three components. 



